24740 + Interview Questions in Mathematics

1.	What is the largest volume of glass tumbler that can exactly measure the volume of two jugs of different volumes which are (x2+5x+p) and (x2+3x+q) if p and q are constants?
Answer» What is the largest volume of glass tumbler that can exactly measure the volume of two jugs of different volumes which are $(x^{2} + 5 x + p)$ and $(x^{2} + 3 x + q)$ if p and q are constants?

Discussion

2.	The ends A, B of a straight line segment of constant length c slides on the fixed rectangular axes OX, OY respectively. If the rectangle OAPB be completed. Then the locus of the foot of the perpendicular drawn from P upon AB is
Answer» The ends A, B of a straight line segment of constant length c slides on the fixed rectangular axes OX, OY respectively. If the rectangle OAPB be completed. Then the locus of the foot of the perpendicular drawn from P upon AB is

Discussion

3.	The following table gives the marks obtained by the students of a class in an exam out of 50. MarksNo. of StudentsBelow 105Below 2010Below 3023Below 4031Below 5040(i) Convert the cumulative frequency distribution into a regular frequency distribution.(ii) Find the mean. [3 MARKS]
Answer» The following table gives the marks obtained by the students of a class in an exam out of 50. $\begin{matrix} Marks & No. of Students B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 40 \end{matrix}$ (i) Convert the cumulative frequency distribution into a regular frequency distribution. (ii) Find the mean. [3 MARKS]

Discussion

4.	Factorise:2 – 50x2
Answer» Factorise: 2 – 50x²

Discussion

5.	Find the values of following polynomials at m=−1,n=0 and p=1:(i) m+n+p(ii) m2n2+n2p2+p2m2
Answer» Find the values of following polynomials at $m = - 1, n = 0$ and $p = 1$ : (i) $m + n + p$ (ii) $m^{2} n^{2} + n^{2} p^{2} + p^{2} m^{2}$

Discussion

6.	Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surfaces areas of the three cubes.
Answer» Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surfaces areas of the three cubes.

Discussion

7.	Question 1 (ii)Solve the following pair of linear equations by the substitution method.s−t=3;s3+t2=6
Answer» Question 1 (ii) Solve the following pair of linear equations by the substitution method. $s - t = 3; \frac{s}{3} + \frac{t}{2} = 6$

Discussion

8.	In the adjoing figure, what value of x will make AOB, a straight line?
Answer» In the adjoing figure, what value of x will make AOB, a straight line?

Discussion

9.	range of the function 9^x-3^x+1 is
Answer» range of the function 9^x-3^x+1 is

Discussion

10.	In ΔABC,∠A=30∘,∠B=40∘ and ∠C=110∘. The angles of the triangle formed by joining the mid-points of the sides of this triangle are
Answer» In $Δ A B C, ∠ A = 30^{\circ}, ∠ B = 40^{\circ} a n d ∠ C = 110^{\circ}$ . The angles of the triangle formed by joining the mid-points of the sides of this triangle are

Discussion

11.	The value of deteminant ∣∣∣∣a+babaa+ccbcb+c∣∣∣∣ is equal to
Answer» The value of deteminant $∣ ∣∣ ∣ \begin{matrix} a + b & a & b a & a + c & c b & c & b + c \end{matrix} ∣ ∣∣ ∣$ is equal to

Discussion

12.	In the figure given below, P and Q are centres of two circles, intersecting at B and C, and ACD is a straight line.If ∠APB = 150° and ∠BQD = x°, find the value of x.
Answer» In the figure given below, P and Q are centres of two circles, intersecting at B and C, and ACD is a straight line. If ∠APB = 150° and ∠BQD = x°, find the value of x.

Discussion

13.	For what value of k is the polynomial p(x)=2x3−kx2+3x+10 exactly divisible by (x+2)? (a) −13 (b) 13 (c) 3 (d) −3
Answer» For what value of k is the polynomial $p (x) = 2 x^{3} - k x^{2} + 3 x + 10$ exactly divisible by (x+2)? (a) $- \frac{1}{3}$ (b) $\frac{1}{3}$ (c) $3$ (d) $- 3$

Discussion

14.	There are only ___ ways in which a circle and line can interact.
Answer» There are only ___ ways in which a circle and line can interact.

Discussion

15.	Find the value of 10052÷100−12.
Answer» Find the value of $100^{\frac{5}{2}} \div 100^{- \frac{1}{2}}$ .

Discussion

16.	In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.
Answer» In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

Discussion

17.	The value of 5252-4752
Answer» The value of $525^{2}$ - $475^{2}$

Discussion

18.	Factorize: x4 + x2 + 25.
Answer» Factorize: x⁴ + x² + 25.

Discussion

19.	Prove that a triangle must have at least 2 acute angles
Answer» Prove that a triangle must have at least 2 acute angles

Discussion

20.	ABCD is a parallelogram. P is a point on AD such that AP=13AD and Q is a point on BC such that CQ=13BC. Prove that AQCP is a parallelogram.
Answer» $A B C D$ is a parallelogram. $P$ is a point on $A D$ such that $A P = \frac{1}{3} A D$ and Q is a point on $B C$ such that $C Q = \frac{1}{3} B C$ . Prove that $A Q C P$ is a parallelogram.

Discussion

21.	What is the reciprocal of −234?
Answer» What is the reciprocal of $- 2 \frac{3}{4}$ ?

Discussion

22.	If ABCD is a cyclic quadrilateral in which AD \|\| BC (In the given figure). Prove that ∠B = ∠C.
Answer» If ABCD is a cyclic quadrilateral in which AD \|\| BC (In the given figure). Prove that ∠B = ∠C.

Discussion

23.	A chord 6 cm long is 1 cm away from the centre of the circle. What is the length of a chord which is 2 cm away from the centre?
Answer» A chord 6 cm long is 1 cm away from the centre of the circle. What is the length of a chord which is 2 cm away from the centre?

Discussion

24.	The following table gives the life time of 400 neon lamps: Life time (in hours)300−400400−500500−600600−700700−800800−900900−1000Number of lamps14566086746248 A bulb is selected at random. Find the probability that the life time of the selected bulb is: (i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.
Answer» The following table gives the life time of 400 neon lamps: $\begin{matrix} Life time (in hours) & 300 - 400 & 400 - 500 & 500 - 600 & 600 - 700 & 700 - 800 & 800 - 900 & 900 - 1000 Number of lamps & 14 & 56 & 60 & 86 & 74 & 62 & 48 \end{matrix}$ A bulb is selected at random. Find the probability that the life time of the selected bulb is: (i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.

24.

The following table gives the life time of 400 neon lamps: Life time (in hours)300−400400−500500−600600−700700−800800−900900−1000Number of lamps14566086746248 A bulb is selected at random. Find the probability that the life time of the selected bulb is: (i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.

Answer»

The following table gives the life time of 400 neon lamps:

$\begin{matrix} Life time (in hours) & 300 - 400 & 400 - 500 & 500 - 600 & 600 - 700 & 700 - 800 & 800 - 900 & 900 - 1000 Number of lamps & 14 & 56 & 60 & 86 & 74 & 62 & 48 \end{matrix}$

A bulb is selected at random. Find the probability that the life time of the selected bulb is:

(i) less than 400 (ii) between 300 to 800 hours (iii) at least 700 hours.

Discussion

25.	38. What is the formula to find area of scalene triangle and solve this promble in triangle ABC and AB = 5, BC=8 and AC=4. Then area of triangle of ABC
Answer» 38. What is the formula to find area of scalene triangle and solve this promble in triangle ABC and AB = 5, BC=8 and AC=4. Then area of triangle of ABC

Discussion

26.	In simple interest, P = ₹ 4600 ; Amount = ₹ 5600 (at the end of 2 years ),then interest = ₹ ______
Answer» In simple interest, P = ₹ 4600 ; Amount = ₹ 5600 (at the end of 2 years ),then interest = ₹ ______

Discussion

27.	Question 3 A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?
Answer» Question 3 A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Discussion

28.	A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 litres of water ?
Answer» A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 litres of water ?

Discussion

29.	The domain of the function cos−1(2x−1) is
Answer» The domain of the function ${cos}^{- 1} (2 x - 1)$ is

Discussion

30.	D is the midpoint of side BC of ∆ABC and E is the midpoint of BD. If O is the midpoint of AE, prove that ar(∆BOE) = 18ar(∆ABC).
Answer» D is the midpoint of side BC of ∆ABC and E is the midpoint of BD. If O is the midpoint of AE, prove that ar(∆BOE) = $\frac{1}{8}$ ar(∆ABC).

Discussion

31.	(3x+4y+5z)2 = __________________.
Answer» $(3 x + 4 y + 5 z)^{2}$ = __________________.

Discussion

32.	54. LOGARITHM: Value of x, satisfy the equation is A. 50 B. 100 C. 150 D. 200
Answer» 54. LOGARITHM: Value of x, satisfy the equation is A. 50 B. 100 C. 150 D. 200

Discussion

33.	In a triangle ABC, AB = AC and D is a point on side AC such that BC = AC × CD. Prove that BD = BC.
Answer» In a triangle ABC, AB = AC and D is a point on side AC such that BC = AC $\times$ CD. Prove that BD = BC.

Discussion

34.	If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?(a) 25°(b) 30°(c) 45(d) 60°
Answer» If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle? (a) 25° (b) 30° (c) 45 (d) 60°

Discussion

35.	A lawn 20m by 15m is surrounded by a path 2m wide. Area of the path is
Answer» A lawn 20m by 15m is surrounded by a path 2m wide. Area of the path is

Discussion

36.	The probability of any event associated to a random experiment cannot exceed __________.
Answer» The probability of any event associated to a random experiment cannot exceed __________.

Discussion

37.	The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?
Answer» The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?

Discussion

38.	If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is(a) 15 cm(b) 16 cm(c) 17 cm(d) 34 cm
Answer» If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is (a) 15 cm (b) 16 cm (c) 17 cm (d) 34 cm

Discussion

39.	O is the centre of the circle as shown in the figure. If ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm, then what is the measure of ∠ROQ ?
Answer» O is the centre of the circle as shown in the figure. If $∠ O R P = 35^{\circ}$ and the distance between P and Q through 'O' is 4 cm, then what is the measure of $∠ R O Q$ ?

Discussion

40.	Area of an isosceles trapezoid is 77 square inches , the height measures 4 inches and the legs are 5 inches long. find the length of the bases
Answer» Area of an isosceles trapezoid is 77 square inches , the height measures 4 inches and the legs are 5 inches long. find the length of the bases

Discussion

41.	Give expressions for the following cases.(a) Rita scores x marks in Maths and 46 marks in English. What is her total score in Maths and English.(b) The difference of x and 9 where x > 9.(c) The product of a and b added to the difference of a and (a>b).(d) One-half of a multiplied by the sum of x and y.(e) The total distance travelled by a car in x hours at a constant speed of y km/h.(f) The total number of eggs in n cartons if each carton contains k eggs.
Answer» Give expressions for the following cases. (a) Rita scores x marks in Maths and 46 marks in English. What is her total score in Maths and English. (b) The difference of x and 9 where x > 9. $(c) The product of a and b added to the difference of a and (a > b) .$ (d) One-half of a multiplied by the sum of x and y. (e) The total distance travelled by a car in x hours at a constant speed of y km/h. (f) The total number of eggs in n cartons if each carton contains k eggs.

Discussion

42.	What is the angle between(P vector +Q vector) and (P vector - Q vector )
Answer» What is the angle between(P vector +Q vector) and (P vector - Q vector )

Discussion

43.	Two chords AB and CD of a circle intersect at a point outside the circle. Prove thata△PAC~△PDBbPA.PB=PC.PD
Answer» Two chords AB and CD of a circle intersect at a point outside the circle. Prove that $(a) △ PAC ~ △ PDB (b) PA . PB = PC . PD$

Discussion

44.	Question 5 Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side. If intersect they will intersect on the circumcircle of the triangle.
Answer» Question 5 Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side. If intersect they will intersect on the circumcircle of the triangle.

Discussion

45.	Match the following radii of the circle with their corresponding area of the sector if θ = 30°
Answer» Match the following radii of the circle with their corresponding area of the sector if θ = 30°

Discussion

46.	If a, b, c are in G.P. then the value of a-bb-c is equal to ____________.
Answer» If a, b, c are in G.P. then the value of $\frac{a - b}{b - c}$ is equal to ____________.

Discussion

47.	Factorize:x2-3x-6
Answer» Factorize: $x^{2} - \sqrt{3} x - 6$

Discussion

48.	Find the area of the hexagon given below:
Answer» Find the area of the hexagon given below:

48.

Find the area of the hexagon given below:

Answer»

Find the area of the hexagon given below:

Discussion

49.	Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is:
Answer» Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is:

Discussion

50.

The percentage of marks obtained by a student in monthly unit tests are given below: Unit test: I II III IV V Percentage of marks obtained: 69 71 73 68 76 Find the probability that the student gets:(i) more than 70% marks(ii) less than 70% marks(iii) a distinction

Answer» The percentage of marks obtained by a student in monthly unit tests are given below:

Unit test:	I	II	III	IV	V
Percentage of marks obtained:	69	71	73	68	76

Find the probability that the student gets:

(i) more than 70% marks

(ii) less than 70% marks

(iii) a distinction

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the largest volume of glass tumbler that can exactly measure the volume of two jugs of different volumes which are (x2+5x+p) and (x2+3x+q) if p and q are constants?

The ends A, B of a straight line segment of constant length c slides on the fixed rectangular axes OX, OY respectively. If the rectangle OAPB be completed. Then the locus of the foot of the perpendicular drawn from P upon AB is

The following table gives the marks obtained by the students of a class in an exam out of 50. MarksNo. of StudentsBelow 105Below 2010Below 3023Below 4031Below 5040(i) Convert the cumulative frequency distribution into a regular frequency distribution.(ii) Find the mean. [3 MARKS]

Factorise:2 – 50x2

Find the values of following polynomials at m=−1,n=0 and p=1:(i) m+n+p(ii) m2n2+n2p2+p2m2

Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surfaces areas of the three cubes.

Question 1 (ii)Solve the following pair of linear equations by the substitution method.s−t=3;s3+t2=6

In the adjoing figure, what value of x will make AOB, a straight line?

range of the function 9^x-3^x+1 is

In ΔABC,∠A=30∘,∠B=40∘ and ∠C=110∘. The angles of the triangle formed by joining the mid-points of the sides of this triangle are

The value of deteminant ∣∣∣∣a+babaa+ccbcb+c∣∣∣∣ is equal to

In the figure given below, P and Q are centres of two circles, intersecting at B and C, and ACD is a straight line.If ∠APB = 150° and ∠BQD = x°, find the value of x.

For what value of k is the polynomial p(x)=2x3−kx2+3x+10 exactly divisible by (x+2)? (a) −13 (b) 13 (c) 3 (d) −3

There are only ___ ways in which a circle and line can interact.

Find the value of 10052÷100−12.

In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

The value of 5252-4752

Factorize: x4 + x2 + 25.

Prove that a triangle must have at least 2 acute angles

ABCD is a parallelogram. P is a point on AD such that AP=13AD and Q is a point on BC such that CQ=13BC. Prove that AQCP is a parallelogram.

What is the reciprocal of −234?

If ABCD is a cyclic quadrilateral in which AD || BC (In the given figure). Prove that ∠B = ∠C.

A chord 6 cm long is 1 cm away from the centre of the circle. What is the length of a chord which is 2 cm away from the centre?

38. What is the formula to find area of scalene triangle and solve this promble in triangle ABC and AB = 5, BC=8 and AC=4. Then area of triangle of ABC

In simple interest, P = ₹ 4600 ; Amount = ₹ 5600 (at the end of 2 years ),then interest = ₹ ______

Question 3 A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

A vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 litres of water ?

The domain of the function cos−1(2x−1) is

D is the midpoint of side BC of ∆ABC and E is the midpoint of BD. If O is the midpoint of AE, prove that ar(∆BOE) = 18ar(∆ABC).

(3x+4y+5z)2 = __________________.

54. LOGARITHM: Value of x, satisfy the equation is A. 50 B. 100 C. 150 D. 200

In a triangle ABC, AB = AC and D is a point on side AC such that BC = AC × CD. Prove that BD = BC.

If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?(a) 25°(b) 30°(c) 45(d) 60°

A lawn 20m by 15m is surrounded by a path 2m wide. Area of the path is

The probability of any event associated to a random experiment cannot exceed __________.

The perimeter of a right triangle is 24 centimeters. Three times the length of the longer leg minus two times the length of the shorter leg exceeds the hypotenuse by 2 centimeters. What are the lengths of all three sides?

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is(a) 15 cm(b) 16 cm(c) 17 cm(d) 34 cm

O is the centre of the circle as shown in the figure. If ∠ORP=35∘ and the distance between P and Q through 'O' is 4 cm, then what is the measure of ∠ROQ ?

Area of an isosceles trapezoid is 77 square inches , the height measures 4 inches and the legs are 5 inches long. find the length of the bases

What is the angle between(P vector +Q vector) and (P vector - Q vector )

Two chords AB and CD of a circle intersect at a point outside the circle. Prove thata△PAC~△PDBbPA.PB=PC.PD

Question 5 Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side. If intersect they will intersect on the circumcircle of the triangle.

Match the following radii of the circle with their corresponding area of the sector if θ = 30°

If a, b, c are in G.P. then the value of a-bb-c is equal to ____________.

Factorize:x2-3x-6

Find the area of the hexagon given below:

Two adjacent sides of a parallelogram are 51cm and 37cm. One of its diagonals is 20cm, then its area is:

The percentage of marks obtained by a student in monthly unit tests are given below: Unit test: I II III IV V Percentage of marks obtained: 69 71 73 68 76 Find the probability that the student gets:(i) more than 70% marks(ii) less than 70% marks(iii) a distinction